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CHAPTER TWENTY-FOUR

THE MAX, NOT THE METHOD

Henn lie

OUTSTANDING unsolved problems demand new methods for
their solution, while powerful new methods beget new problems
to be solved. But, as Poincare observed, it is the man, not the
method, that solves a problem.
Of old problems responsible for new methods in mathematics
that of motion and all it implies for mechanics, terrestrial and
celestial, may be recalled as one of the principal instigators of
the calculus and present attempts to put reasoning about the
infinite on a firm basis. An example of new problems suggested
by powerful new methods is the swarm which the tensor
calculus, popularized to geometers by its successes in relativity,
let loose in geometry. And finally, as an illustration of Pom-
care's remark, it was Einstein, and not the method of tensors,
that solved the problem of giving a coherent mathematical
account of gravitation. All three theses are sustained in the life
of Charles Hermite, the leading French mathematician of the
second half of the nineteenth century - if we except Hermite's
pupil Poincare, who belonged partly to our own century.
Charles Hermite, born at Dieuze, Lorraine, France, on 24
December 1822 could hardly have chosen a more propitious era
for his birth than the third decade of the nineteenth century.
His was just the rare combination of creative genius and the
ability to master the best in the work of other men which was
demanded in the middle of the century to co-ordinate the
arithmetical creations of Gauss with the discoveries of Abel and
Jacob! in elliptic functionsa the striking advances of Jacobi in
Abelian functions, and the vast theory of algebraic invariants
in process of rapid development by the English mathematicians
Boole, Cayley, and Sylvester.
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